Paulo Gomes and Adelaide Figueiredo
Clustering of Variables Based On a Probabilistic Approach Defined on the Hypersphere
1535 - 1537
2013
7
10
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/17113
https://publications.waset.org/vol/82
World Academy of Science, Engineering and Technology
We consider n individuals described by p standardized variables, represented by points of the surface of the unit hypersphere Sn1. For a previous choice of n individuals we suppose that the set of observables variables comes from a mixture of bipolar Watson distribution defined on the hypersphere. EM and Dynamic Clusters algorithms are used for identification of such mixture. We obtain estimates of parameters for each Watson component and then a partition of the set of variables into homogeneous groups of variables. Additionally we will present a factor analysis model where unobservable factors are just the maximum likelihood estimators of Watson directional parameters, exactly the first principal component of data matrix associated to each group previously identified. Such alternative model it will yield us to directly interpretable solutions (simple structure), avoiding factors rotations.
Open Science Index 82, 2013